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A general multivariate threshold GARCH model with dynamic conditional correlations

  • Francesco Audrino

    ()

  • Fabio Trojani

    ()

We propose a new multivariate GARCH model with Dynamic Conditional Correlations that extends previous models by admitting multivariate thresholds in conditional volatilities and correlations. The model estimation is feasible in large dimensions and the positive deniteness of the conditional covariance matrix is easily ensured by the structure of the model. Thresholds in conditional volatilities and correlations are estimated from the data, together with all other model parameters. We study the performance of our model in three distinct applications to US stock and bond market data. Even if the conditional volatility functions of stock returns exhibit pronounced GARCH and threshold features, their conditional correlation dynamics depends on a very simple threshold structure with no local GARCH features. We obtain a similar result for the conditional correlations between government and corporate bond returns. On the contrary, we ¯nd both threshold and GARCH structures in the conditional correlations between stock and government bond returns. In all applications, our model improves signi¯cantly the in-sample and out-of-sample forecasting power for future conditional correlations with respect to other relevant multivariate GARCH models.

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Paper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2007 with number 2007-25.

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Length: 34 pages
Date of creation: Apr 2007
Date of revision:
Handle: RePEc:usg:dp2007:2007-25
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  1. Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003. "Flexible Multivariate GARCH Modeling with an Application to International Stock Markets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 735-747, August.
  2. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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  7. Kim, S.W. & Rogers, J.H., 1993. "International Stock Price Spillovers and Market Liberalization: Evidence from Korea, Japan, and the United States," Papers 4-93-7, Pennsylvania State - Department of Economics.
  8. Adrian Pagan, 1985. "Two Stage and Related Estimators and Their Applications," Cowles Foundation Discussion Papers 741, Cowles Foundation for Research in Economics, Yale University.
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  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  12. Fulvio Corsi & Francesco Audrino, 2007. "Realized Correlation Tick-by-Tick," University of St. Gallen Department of Economics working paper series 2007 2007-02, Department of Economics, University of St. Gallen.
  13. Robert F. Engle & Takatoshi Ito & Wen-Ling Lin, 1988. "Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market," NBER Working Papers 2609, National Bureau of Economic Research, Inc.
  14. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  15. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  16. Bae, Kee-Hong & Andrew Karolyi, G., 1995. "Good news, band news and international spilovers of stock return volatility between Japan and the U.S," Pacific-Basin Finance Journal, Elsevier, vol. 3(1), pages 144-144, May.
  17. Fabio Trojani & Francesco Audrino, 2006. "Estimating and predicting multivariate volatility thresholds in global stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 345-369.
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